document.write( "Question 1083768: Two cars are travelling on horizontal roads in straight lines, car A at
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Algebra.Com's Answer #698020 by ikleyn(52864) $\"\"$ $\"About$

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\n" ); document.write( "Two cars are travelling on horizontal roads in straight lines, car A at
\n" ); document.write( "70 km/h at $\"highlight%28cross%28800%29%29\"$ 80° and car B at 50 km/h at 120°.
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document.write( "Let O be the origin of the coordinate system O = (0,0),\r\n" );
document.write( "OA is the segment corresponding to the location of the car A and OB be the segment corresponding to the location of the car B.\r\n" );
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document.write( "|OA| = 70*t kilometers,\r\n" );
document.write( "|OB| = 50*t kilometers, where t is time in hours.\r\n" );
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document.write( "Apply the cosine law to determine the length of the segment AB (this length is the distance between the two cars).\r\n" );
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document.write( "Notice that the angle between OA and OB is 120° - 80° = 40°.\r\n" );
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document.write( "|AB| =  = \r\n" );
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document.write( "     =  = \r\n" );
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document.write( "     = .     (1)\r\n" );
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document.write( "You see that the distance |AB| is proportional to the time.\r\n" );
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document.write( "Hence, the square root, which is the second multiplier in the formula (1), is the rate of the distance change, i.e. relative velocity, \r\n" );
document.write( "which is under the question.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. The relative velocity between the two cars is $\"sqrt%2870%5E2+%2B+50%5E2+-+2%2A70%2A50%2Acos%2840%5Eo%29%29\"$ kilometers per hour.\r
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